Dyadic Synthesis Filter Bank

Library

Filtering / Multirate Filters

dspmlti4

Description

Note
This block always does frame-based processing, and its inputs
must be of certain sizes. To use input subbands that do not fit the
criteria of this block, use the Two-Channel
Synthesis Subband Filter block. (You can connect multiple
copies of the Two-Channel Synthesis Subband Filter block to create
a multilevel dyadic synthesis filter bank.)

You can configure this block to compute the inverse discrete
wavelet transform (IDWT) or reconstruct a signal from subbands with
smaller bandwidths and slower sample rates. When the block computes
the inverse discrete wavelet transform (IDWT) of the input, the output
has the same dimensions as the input. Each column of the output is
the IDWT of the corresponding input column. When reconstructing a
signal, the block uses a series of highpass and lowpass FIR filters
to reconstruct the signal from the input subbands, as illustrated
in Wavelet Filter Banks (the Asymmetric
one). The reconstructed signal has a wider bandwidth and faster sample
rate than the input subbands.

You can specify the filter bank's highpass and lowpass filters
by providing vectors of filter coefficients. You can do so directly
on the block mask, or, if you have a Wavelet Toolbox™ license,
you can specify wavelet-based filters by selecting a wavelet from
the Filter parameter. You must set the filter
bank structure to asymmetric or symmetric, and specify the number
of levels in the filter bank.

When you set the Input parameter to Multiple
ports, you must provide each subband to the block through
a different input port as a vector or matrix. You should input the
highest frequency band through the topmost port. When you set the Input parameter
to Single port, the block input must be
a vector or matrix of concatenated subbands.

Note
To use a dyadic synthesis filter bank to perfectly reconstruct
the output of a dyadic analysis filter bank, the number of levels
and tree structures of both filter banks must be
the same. In addition, the filters in the synthesis filter bank must be
designed to perfectly reconstruct the outputs of the analysis filter
bank. Otherwise, the reconstruction is not perfect.

This block automatically computes wavelet-based perfect reconstruction
filters when the wavelet selection in the Filter parameter
of this block is the same as the Filter parameter
setting of the corresponding Dyadic Analysis
Filter Bank block. The use of wavelets requires a Wavelet Toolbox license.
To learn how to design your own perfect reconstruction filters, see References.

Input Requirements

The inputs to this block are usually the outputs of a Dyadic Analysis Filter Bank block. Since the
Dyadic Analysis Filter Bank block can output from either a single
port or multiple ports, the Dyadic Synthesis Filter Bank block accepts
inputs to either a single port or multiple ports.

The Input parameter sets whether the block
accepts inputs from a single port or multiple ports, and thus determines
the input requirements, as summarized in the following lists and figure.

Note:
Any output of a Dyadic Analysis Filter Bank block whose parameter
settings match the corresponding settings of this block is a valid
input to this block. For example, the setting of the Dyadic Analysis
Filter Bank block parameter, Output, must be
the same as this block's Input parameter (Single
port or Multiple ports).

Valid Inputs for Input Set to Single Port

Inputs must be vectors or matrices of concatenated
subbands. The block always interprets the inputs as sample based.

Wavelet Filter Banks

Filter Bank Filters

You must specify the highpass and lowpass filters in the filter
bank by setting the Filter parameter to one of
the following options:

User defined — Allows
you to explicitly specify the filters with two vectors of filter coefficients
in the Lowpass FIR filter coefficients and Highpass
FIR filter coefficients parameters. The block uses the
same lowpass and highpass filters throughout the filter bank. The
two filters should be halfband filters, where each filter passes the
frequency band that the other filter stops. To use this block to perfectly
reconstruct a signal decomposed by a Dyadic
Analysis Filter Bank block, the filters in this block must be
designed to perfectly reconstruct the outputs of the analysis filter
bank. To learn how to design your own perfect reconstruction filters,
see References.

Wavelet such as Biorthogonal or Daubechies —
The block uses the specified wavelet to construct the lowpass and
highpass filters using the Wavelet Toolbox function wfilters.
Depending on the wavelet, the block might enable either the Wavelet
order or Filter order [synthesis / analysis] parameter.
(The latter parameter allows you to specify different wavelet orders
for the analysis and synthesis filter stages.) To use this block to
reconstruct a signal decomposed by a Dyadic
Analysis Filter Bank block, you must set both blocks to use
the same wavelets with the same order. You must have a Wavelet Toolbox license
to use wavelets.

Examples

Dialog Box

The parameters displayed in the block dialog vary depending
on the setting of the Filter parameter. Only
some of the parameters described below are visible in the dialog box
at any one time.

Note
To use this block to reconstruct a signal decomposed by a Dyadic Analysis Filter Bank block, all the
parameters in this block must be the same as the corresponding parameters
in the Dyadic Analysis Filter Bank block (except the Lowpass
FIR filter coefficients and Highpass FIR filter
coefficients; see the descriptions of these parameters).

Filter

The type of filter used to determine the high- and low-pass
FIR filters in the filter bank:

Select a wavelet such as Biorthogonal or Daubechies to
specify a wavelet-based filter. The block uses the Wavelet Toolbox wfilters function
to construct the filters. Extra parameters such as Wavelet
order or Filter order [synthesis / analysis] might
become enabled. For a list of the supported wavelets, see the table Specifying Filters with the Filter Parameter and
Related Parameters.

Lowpass FIR filter
coefficients

A vector of filter coefficients (descending powers of z)
that specifies coefficients used by all the lowpass filters in the
filter bank. This parameter is enabled when you set Filter to User
defined. The lowpass filter should be a half-band filter
that passes the frequency band stopped by the filter specified in
the Highpass FIR filter coefficients parameter.
To perfectly reconstruct a signal decomposed by the Dyadic
Analysis Filter Bank, the filters in this block must be
designed to perfectly reconstruct the outputs of the analysis filter
bank. Otherwise, the reconstruction is not perfect. The default values
of this parameter specify a perfect reconstruction filter for the
default settings of the Dyadic Analysis Filter Bank (based on a Daubechies
wavelet with wavelet order 3).

Highpass FIR filter
coefficients

A vector of filter coefficients (descending powers of z)
that specifies coefficients used by all the highpass filters in the
filter bank. This parameter is enabled when you set Filter to User
defined. The highpass filter should be a half-band filter
that passes the frequency band stopped by the filter specified in
the Lowpass FIR filter coefficients parameter.
To perfectly reconstruct a signal decomposed by the Dyadic
Analysis Filter Bank, the filters in this block must be
designed to perfectly reconstruct the outputs of the analysis filter
bank. Otherwise, the reconstruction is not perfect. The default values
of this parameter specify a perfect reconstruction filter for the
default settings of the Dyadic Analysis Filter Bank (based on a Daubechies
wavelet with wavelet order 3).

The order of the wavelet for the synthesis and analysis filter
stages. For example, when you set the Filter parameter
to Biorthogonal and set the Filter
order [synthesis / analysis] parameter to [2 /
6], the block calls the wfilters function
with input argument 'bior2.6'. This parameter is
enabled only when you set Filter to certain types
of wavelets, as shown in Specifying Filters with the Filter Parameter and
Related Parameters.

Number
of levels

The number of filter bank levels. An n-level
asymmetric structure has n+1 inputs, and an n-level
symmetric structure has 2n inputs,
as shown in Wavelet Filter Banks.

The default setting of this parameter is Asymmetric for
the Dyadic Synthesis Filter Bank block, and Symmetric for
the IDWT block.

Input

Set to Multiple ports to accept each
input subband at a separate port (the topmost port accepts the subband
with the highest frequency band). Set to Single port to
accept one vector or matrix of concatenated subbands at a single port.
For more information, see Input Requirements.

The default setting of this parameter is Multiple
ports for the Dyadic Synthesis Filter Bank block, and Single
port for the IDWT block.